CHICAGO—The world’s largest exchange company is struggling to keep up with tariffs and a surge in global crop production that is reshaping agricultural trading.

CME Group Inc., whose antecedents helped invent futures contracts in the 19th Century, ties its main agricultural products to the value of American crops. And while CME’s futures have grown, some say the exchange risks missing out on the boom in countries including Russia and Brazil, which now export more of some agricultural goods than the U.S.